In a vessel, the ideal gas is at a pressure $$\mathrm{P}$$. If the mass of all the molecules is halved and their speed is doubled, then resultant pressure of the gas will be

The average force applied on the walls of a closed container depends on $$T^x$$ where $$T$$ is the temperature of an ideal gas. The value of '$$x$$' is

A black body radiates maximum energy at wavelength '$$\lambda$$' and its emissive power is $$\mathrm{E}$$. Now due to change in temperature of that body, it radiates maximum energy at wavelength $$\frac{2 \lambda}{3}$$. At that temperature emissive power is

A Carnot engine with efficiency $$50 \%$$ takes heat from a source at $$600 \mathrm{~K}$$. To increase the efficiency to $$70 \%$$, keeping the temperature of the sink same, the new temperature of the source will be